Here is how I make soft boiled eggs, coming from a place where soft boiled eggs are a breakfast staple. Works for me every time, without any problems of cracked eggs either.
Place your eggs [large to extra large, straight out of the refrigerator, ] in one layer in a pot not much bigger than the amount of eggs you want to cook. Cover them just barely with cold water, and heat on high till boiling[ no lid]. Turn heat down to simmer and continue to cook for 3 -3 1/2 minutes [3 min if you like your egg white still a little bit soft near the yolk, 3 1/2 min if you want to make sure the egg white is hardened all over]. Replace boiling water with cold water till eggs are warm, not hot [to the same effect as moving them to ice water]. Eat warm, out of the shell.

Learned this from my polish mom! I use large eggs right out of the fridge and get a pan of water boiling just enough to cover the egg. I then take a push pin and make a hole in one end and then when boiling place the egg gently in the water. I cook if for exactly 6 minutes and then take it out and a quick rinse in cold water so I can touch it and then peel and eat! I've been doing it this way for over 30 years and always have perfect soft boiled eggs with cooked whites and runny yellow. I put them on toast or an english muffin!

The trick of making a very small hole with a pin (in the end) lets the gas escape - especially the sulphur. In the case of hardboiled eggs, this also keeps them from getting that green/blue color on the white.

putting a hole in the _large_ end of the egg allows the pocket of gas that accumulates there as an egg ages to expand without causing - or furthering pre-existing - cracking of the shell.

eggs contain sulfur. eggs contain iron.
it is the mixture of those two elements at the white/yolk interface that produces the greenish ring when overcooked or kept hot too long or kept cold really too long.

so for the theory that the sulfur collects in the pocket to be true:
(a) it has to migrate out of the egg "innards"
(b) penetrate the membrane and collect in the pocket.
(c) upon being cooked, and not being released it has to
(d) penetrate the membrane, now going backwards
(so,,, if it likes it so much inside the egg, why did it leave?)
(e) migrate back into the egg
(f) find some iron to bind

Tried your way twice and both times, my egg whites are still very loose. Can hardly even get shell off without taking some semi-solid egg white with it. Your pot must retain a lot more heat than mine do. I'm going to stick with the old cold water, bring to a boil routine.

I steam my eggs for 7 minutes. The results are the same. Why heat all that water? The same applies to corn on the cob. Just add enough water to the pot to get through the cooking time which is 4 minutes for corn. You will save alot of energy. Also, you can turn off the heat with a minute remaining if you use an electric burner.

Here's how I make soft-boiled eggs every morning. I am too busy to give it too much thought or effort.

Put two refrigerated eggs in an empty saucepan.
Fill the saucepan with water until it covers the eggs.
Place the pan on the burner and crank it up to "high" heat. (Note that I have an old coil burner stove top.)
Set a kitchen timer for 12 minutes. (You will not need as much time if you have a gas or ceramic cooktop.)
Then I walk away.

When the timer dings I transfer the eggs to a bowl of ice water and set the bowl in the refrigerator for about 30 minutes while I finish getting ready for work.

I pull them out of the fridge on my way out the door and enjoy them with fruit and coffee at my desk.

And that, my friends, is how a workin' woman does it.

P.S. - I like the idea of boiling the water, then removing it from the heat, and placing the eggs in. Then it doesn't matter what kind of cooktop you have. I'll have to try that method sometime.

I love the STEAMING idea someone posted and will try that later this week. A few others debate the amount of water needed to boil and I agree that a little less than fully covered will work, adding a suggestion to stir them so all sides cook, but I DISAGREE with the person who wrote something about older eggs being better to use because they float allowing them to avoid hitting the bottom - when this way actually causes them to hit each other or the sides from the boiling bubbles. The simple solution is to not let the heat get as hot as I usually do I suppose but I guess this problem is only for hard cooked or if you like to set and forget like me sometimes.

As gigelus2k3 notes the optimum time window to have a hard-boiled white and runny yoke is very narrow. In experimenting around the world, indoors and outdoors, over many years I was trying to put a list of the variables together so that I could deduce a basic equation for determining the timings rather than have to experiment for a few weeks every time I move to a new location. (I have boiled eggs in various climates, altitudes, terrains (apartments to deserts, camps to hotel suites etc. and timings can vary from 4 minutes to 6 minutes 20 seconds).
With a colleague, recently in a desert location, altitude 2,100m, ambient temperature 42degC, it took a number of iterations to get this right and, in winter, temperature -2degC it changed (unfortunately we were not recording the atmospheric pressure (silly, I know but the meteo data gatherer was not installed!).
So here is a list of variables (with the aim to boil and cool at outside temperature, ice baths being impractical everywhere) that could affect timings:
Altitude
Ambient temperature (? dubious since we are just concerned with boiling water ?)
Atmospheric pressure
Humidity (?)
Egg temperature on water drop entry
Egg volume (? or ratio of length to width "circumference" ?)
Water salinity

I love the STEAMING idea someone posted and will try that later this week. . . .

SUPPERMAN, I also steam my "hard-boiled" eggs and now really like them that way (didn't like the "rubbery" texture of the whites when boiling them in water--tried various ways).
I think I use 6 min rather than 7 as mentioned, but the size of the egg and coldness matters too; they're all good.
Here's what I wrote about that before in a post about peeling eggs:

. . Wanted to add though that steaming eggs creates whites that are much less rubbery and firm than boiling . . . They're quite "tender," in fact.

I've eaten lots more "hard-boiled" eggs since discovering that... never been a fan of tasteless/rubbery eggwhites.
Chopping just one steamed egg (I cheat with two cutting orientations in an egg slicer) then mixing in some mayo and a bit of salt makes a really delicious and quick egg salad sandwich on toast.

my technique:
...poke a hole in the large end of the egg or eggs
...lay in a shallow bowl
...put bowl in a bamboo steamer** over boiling water (lid on) to cook
...remove with tongs/etc and eat, or cool
(**works with any kind of kludgy steaming setup though)
.

heat will flow from a hotter area to a cooler area
the rate at which heat flows depends on:
- temperature difference
- coefficients of thermal conductivity
- the shell has one coefficient
- the membrane has one coefficient
- the white has one coefficient
- the yoke has one coefficient
don't know for fact, but I suspect that the coefficient of thermal conductivity for the white and the yoke may change as they solidify . . .

the rate is how many BTU/area will flow over time.
so the surface area of the egg determines how many absolute BTU enter the insides over time.

presuming the 'whole egg' is at the same temperature, one could calculate how many BTU is needed to raise the temperature of the mass of the white and the mass of the yolk to the desired temperature, and how many BTU 'get wasted' heating up the shell and the membrane via the the (four) coefficients of thermal capacitance - which determines how many BTU/mass is required to raise the temperature per degree.

if the egg is left out on the counter for some time, it's no longer at a uniform temperature.
makes things yet more complicated.

so if you know:
- the temperature of the cooking medium
- the temperature of the uncooked egg
- egg surface area
- interior mass, by component
- all the coefficients
- what end point temperature you desire
then the calculations are straightforward.

although altitude/atmospheric pressure does affect the boiling point of water - and its resulting steam - but it's probably easier to measure the temperature of the cooking medium vs atmospheric pressure when camping.

measuring the temperature of the medium also negates the concern of salinity/mineral content of water - which does affect its boiling point.

after the initial calculations, one has to loop back to the question of rubbery whites.
if the cooking medium is too hot, the temperature gradient from the outside to the center is too great - yoke may be perfect, but the white got too hot and went rubbery.....

the solution is quite simple, options are:
(a) reduce the temperature of the cooking medium and recalculate the timing (this I suspect is the secret behind the steaming technique)
(b) increase the temperature of the uncooked egg and recalculate the timing.

pretty simple - most any teenager could probably write an app for that . . . .

I followed these instructions *exactly* and I wasted four "large" eggs. This is FAR too short of a time to get soft boiled eggs. Furthermore, letting eggs sit in non-boiling water cooks them at an incredibly slow rate and most importantly, is a pointless exercise.

If you want to waste eggs, use this method.

If you want regular soft boiled eggs follow the directions on any number of millions of google results.

Been working on this for a few days now. Altitude, altitude, altitude!!!!!! You have to figure out your cooking time at your altitude AND in your water!!!!! At 6207 ft above sea level AND in my water 12 minutes seems to be my magic time after I set the "from ref eggs" into the boiling water and then remove from heat and cover.
Thank you for the article!!!!!